Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112785
Hao Yu , Zhe Guan , Toru Yamamoto , Junzheng Wang
This paper studies sampled-data tracking control problems for first-order nonlinear time-invariant plants. A sampled-data adaptive PI controller is developed from exact discretization and full form dynamic linearization (FFDL) methods. To ensure the uniform boundedness of adaptive PI parameters with respect to sufficiently small sampling periods, novel lifted FFDL models and cost functions are introduced for designing controllers and adaptive rules. After establishing nonlinear closed-loop dynamics, new overall Lyapunov functions containing logarithmic operation are constructed for proving global stability and convergence. An extension to locally Lipschitz dynamics is given. Finally, two numerical examples and a practical application in longitudinal speed tracking for electrical cars are simulated to illustrate the efficiency and feasibility of the proposed results.
{"title":"FFDL-based sampled-data adaptive PI control with uniformly bounded parameters","authors":"Hao Yu , Zhe Guan , Toru Yamamoto , Junzheng Wang","doi":"10.1016/j.automatica.2025.112785","DOIUrl":"10.1016/j.automatica.2025.112785","url":null,"abstract":"<div><div>This paper studies sampled-data tracking control problems for first-order nonlinear time-invariant plants. A sampled-data adaptive PI controller is developed from exact discretization and full form dynamic linearization (FFDL) methods. To ensure the uniform boundedness of adaptive PI parameters with respect to sufficiently small sampling periods, novel lifted FFDL models and cost functions are introduced for designing controllers and adaptive rules. After establishing nonlinear closed-loop dynamics, new overall Lyapunov functions containing logarithmic operation are constructed for proving global stability and convergence. An extension to locally Lipschitz dynamics is given. Finally, two numerical examples and a practical application in longitudinal speed tracking for electrical cars are simulated to illustrate the efficiency and feasibility of the proposed results.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112785"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799605","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112766
Yan-Jun Liu, Wenguang Zan, Li Tang
This study explores the event-triggered based output feedback consensus issue for multi-agent systems (MASs) under denial-of-service (DoS) attacks. All agents in the considered systems are governed by parabolic partial differential equations (PDEs). Faced with unpredictable system states and malicious attackers launching non-periodic DoS attacks, an event-triggered security control agreement for MASs is introduced and achieve consensus on any given undirected communication graph. The tolerable frequency and duration of DoS attacks are outlined in relation to the observer-based security consensus problem. By employing Lyapunov technique and mathematical inequalities, the sufficient conditions to ensure the global asymptotic stability of MASs under DoS attacks are given. Furthermore, a rigorous demonstration of the minimum dwell time between successive triggered events is furnished. Finally, simulation examples effectively validate the theoretical findings.
{"title":"DoS attacks in parabolic multi-agent systems: An output feedback based event-triggered control approach","authors":"Yan-Jun Liu, Wenguang Zan, Li Tang","doi":"10.1016/j.automatica.2025.112766","DOIUrl":"10.1016/j.automatica.2025.112766","url":null,"abstract":"<div><div>This study explores the event-triggered based output feedback consensus issue for multi-agent systems (MASs) under denial-of-service (DoS) attacks. All agents in the considered systems are governed by parabolic partial differential equations (PDEs). Faced with unpredictable system states and malicious attackers launching non-periodic DoS attacks, an event-triggered security control agreement for MASs is introduced and achieve consensus on any given undirected communication graph. The tolerable frequency and duration of DoS attacks are outlined in relation to the observer-based security consensus problem. By employing Lyapunov technique and mathematical inequalities, the sufficient conditions to ensure the global asymptotic stability of MASs under DoS attacks are given. Furthermore, a rigorous demonstration of the minimum dwell time between successive triggered events is furnished. Finally, simulation examples effectively validate the theoretical findings.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112766"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112746
Kaikai Zheng , Dawei Shi , Sandra Hirche , Yang Shi
Learning-based control has attracted significant attention in recent years, especially for plants that are difficult to model based on first-principles. A key issue in learning-based control is how to make efficient use of data as the abundance of data becomes overwhelming. To address this issue, this work proposes an information-triggered learning framework and a corresponding learning-based controller design approach with guaranteed stability. Specifically, we consider a linear time-invariant system with unknown dynamics. A set-membership approach is introduced to learn a parametric uncertainty set for the unknown dynamics. Then, a data selection mechanism is proposed by evaluating the incremental information in a data sample, where the incremental information is quantified by its effects on shrinking the parametric uncertainty set. Next, after introducing a stability criterion using the set-membership estimate of the system dynamics, a robust learning-based predictive controller (LPC) is designed by minimizing a worst-case cost function. The closed-loop stability of the LPC equipped with the information-triggered learning protocol is discussed within a high-probability framework. Finally, comparative numerical experiments are performed to verify the validity of the proposed approach.
{"title":"Information-triggered learning with application to learning-based predictive control","authors":"Kaikai Zheng , Dawei Shi , Sandra Hirche , Yang Shi","doi":"10.1016/j.automatica.2025.112746","DOIUrl":"10.1016/j.automatica.2025.112746","url":null,"abstract":"<div><div>Learning-based control has attracted significant attention in recent years, especially for plants that are difficult to model based on first-principles. A key issue in learning-based control is how to make efficient use of data as the abundance of data becomes overwhelming. To address this issue, this work proposes an information-triggered learning framework and a corresponding learning-based controller design approach with guaranteed stability. Specifically, we consider a linear time-invariant system with unknown dynamics. A set-membership approach is introduced to learn a parametric uncertainty set for the unknown dynamics. Then, a data selection mechanism is proposed by evaluating the incremental information in a data sample, where the incremental information is quantified by its effects on shrinking the parametric uncertainty set. Next, after introducing a stability criterion using the set-membership estimate of the system dynamics, a robust learning-based predictive controller (LPC) is designed by minimizing a worst-case cost function. The closed-loop stability of the LPC equipped with the information-triggered learning protocol is discussed within a high-probability framework. Finally, comparative numerical experiments are performed to verify the validity of the proposed approach.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112746"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112795
Alexander Yu. Pogromsky , Alexey S. Matveev
This paper addresses the problem of robust remote state estimation for uncertain nonlinear discrete-time systems when sensor data are transmitted through a digital communication channel of finite bit-rate capacity. The goal is to determine the minimal channel rate required to guarantee a prescribed estimation accuracy in the presence of bounded model uncertainty. We derive an explicit, tractable lower bound on the channel bit rate that ensures this accuracy for any admissible uncertainty level. The bound highlights the fundamental role of the accuracy-to-uncertainty ratio in remote estimation. The analysis relies on a quadratic dissipation inequality describing system uncertainty within the framework of incremental input-to-state stability, leading to a constructive Lyapunov-based characterization. The proposed conditions admit a closed-form analytical expression for a class of systems, including the uncertain Lozi map, which serves as an illustrative example.
{"title":"Remote robust state estimation for nonlinear systems","authors":"Alexander Yu. Pogromsky , Alexey S. Matveev","doi":"10.1016/j.automatica.2025.112795","DOIUrl":"10.1016/j.automatica.2025.112795","url":null,"abstract":"<div><div>This paper addresses the problem of robust remote state estimation for uncertain nonlinear discrete-time systems when sensor data are transmitted through a digital communication channel of finite bit-rate capacity. The goal is to determine the minimal channel rate required to guarantee a prescribed estimation accuracy in the presence of bounded model uncertainty. We derive an explicit, tractable lower bound on the channel bit rate that ensures this accuracy for any admissible uncertainty level. The bound highlights the fundamental role of the accuracy-to-uncertainty ratio in remote estimation. The analysis relies on a quadratic dissipation inequality describing system uncertainty within the framework of incremental input-to-state stability, leading to a constructive Lyapunov-based characterization. The proposed conditions admit a closed-form analytical expression for a class of systems, including the uncertain Lozi map, which serves as an illustrative example.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112795"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784445","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
On-orbit useful lifetime is a critical metric for spacecraft missions, for which we propose a maximum-system-reliability control allocation scheme for spacecraft with redundant actuators. The dynamic reliability model for the redundant actuator system is formulated, incorporating an online parameter estimation method initialized with offline estimates. On this basis, we define a control allocation optimization problem that maximizes the one-step system reliability prediction. To enable efficient online computation, a recursive optimization algorithm is introduced. Theoretical analysis proves that the proposed approach can extend the useful lifetime of the redundant actuator system with any failure mode. A comparative example of spacecraft attitude stabilization validates the feasibility, generality, and superiority of the proposed method.
{"title":"Maximum-system-reliability control allocation for spacecraft with redundant actuators","authors":"Jianchun Zhang , Xiang Yu , Jianzhong Qiao , Lei Guo","doi":"10.1016/j.automatica.2025.112779","DOIUrl":"10.1016/j.automatica.2025.112779","url":null,"abstract":"<div><div>On-orbit useful lifetime is a critical metric for spacecraft missions, for which we propose a maximum-system-reliability control allocation scheme for spacecraft with redundant actuators. The dynamic reliability model for the redundant actuator system is formulated, incorporating an online parameter estimation method initialized with offline estimates. On this basis, we define a control allocation optimization problem that maximizes the one-step system reliability prediction. To enable efficient online computation, a recursive optimization algorithm is introduced. Theoretical analysis proves that the proposed approach can extend the useful lifetime of the redundant actuator system with any failure mode. A comparative example of spacecraft attitude stabilization validates the feasibility, generality, and superiority of the proposed method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112779"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112772
Juntao Li , Cong Liang , Deyuan Meng
Designing superior distributed algorithms for solving linear algebraic equations (LAEs) plays a crucial role in engineering and computer science fields. This paper proposes two discrete distributed algorithms for solving LAEs from the perspective of optimal control. By benefiting from the devised error system and constructed performance index, the presented algorithms can converge R-linearly to a solution of LAEs without solving algebraic Riccati equations. In particular, the full-row rank requirements on sub-matrices are eliminated in row partitioning framework. Moreover, the need for communication exchange among all agents within the same cluster is alleviated, and only one state variable is updated in the row-wise arbitrary column partitioning framework. Simulation results demonstrate that the proposed distributed algorithms outperform non-optimal control design algorithms in terms of convergence performance.
{"title":"Distributed algorithms for solving linear algebraic equations: An optimal control perspective","authors":"Juntao Li , Cong Liang , Deyuan Meng","doi":"10.1016/j.automatica.2025.112772","DOIUrl":"10.1016/j.automatica.2025.112772","url":null,"abstract":"<div><div>Designing superior distributed algorithms for solving linear algebraic equations (LAEs) plays a crucial role in engineering and computer science fields. This paper proposes two discrete distributed algorithms for solving LAEs from the perspective of optimal control. By benefiting from the devised error system and constructed performance index, the presented algorithms can converge R-linearly to a solution of LAEs without solving algebraic Riccati equations. In particular, the full-row rank requirements on sub-matrices are eliminated in row partitioning framework. Moreover, the need for communication exchange among all agents within the same cluster is alleviated, and only one state variable is updated in the row-wise arbitrary column partitioning framework. Simulation results demonstrate that the proposed distributed algorithms outperform non-optimal control design algorithms in terms of convergence performance.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112772"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112790
Julian D. Schiller, Matthias A. Müller
We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori verification of a particular excitation condition for the parameters. Instead, we use online information about the actual excitation of the parameters at any time during operation and ensure that the regularization term in the cost function is always automatically selected appropriately. This ensures that the state and parameter estimation error is bounded for all times, even if the parameters are never (or only rarely) excited during operation. Robust exponential stability of the state and parameter estimation error emerges under an additional uniform condition on the maximum duration of insufficient excitation. The theoretical results are illustrated by a numerical example.
{"title":"Nonlinear moving horizon estimation for robust state and parameter estimation","authors":"Julian D. Schiller, Matthias A. Müller","doi":"10.1016/j.automatica.2025.112790","DOIUrl":"10.1016/j.automatica.2025.112790","url":null,"abstract":"<div><div>We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the <em>a priori</em> verification of a particular excitation condition for the parameters. Instead, we use online information about the actual excitation of the parameters at any time during operation and ensure that the regularization term in the cost function is always automatically selected appropriately. This ensures that the state and parameter estimation error is bounded for all times, even if the parameters are never (or only rarely) excited during operation. Robust exponential stability of the state and parameter estimation error emerges under an additional uniform condition on the maximum duration of insufficient excitation. The theoretical results are illustrated by a numerical example.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112790"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112791
Zhenhua Deng, Cong Liu
This paper studies constrained noncooperative games (NGs), which take the general linear dynamics of players into account. In the formulation, each player has local convex set constraints, and all players are restricted by coupling nonlinear inequality constraints. Notably, the majority of existing results for NGs with physical systems do not involve local constraints, let alone general convex sets. Besides, nearly all of related results cannot guarantee local constraints to be satisfied all the time, because physical players cannot control their decisions directly due to system dynamics. Here we develop a distributed adaptive strategy on the basis of gradient descent, projection operators, primal–dual methods and state feedback. The strategy is fully distributed. We analyze the strategy via variational analysis and Lyapunov theory. With our strategy, the players seek the exact variational generalized Nash equilibrium (v-GNE), and always satisfy local constraints, in contrast to existing results. Lastly, our method is applied to the electricity market games of doubly-fed induction generators.
{"title":"Distributed local-constraint-satisfied strategy for noncooperative games of autonomous general linear players and its application to smart grids","authors":"Zhenhua Deng, Cong Liu","doi":"10.1016/j.automatica.2025.112791","DOIUrl":"10.1016/j.automatica.2025.112791","url":null,"abstract":"<div><div>This paper studies constrained noncooperative games (NGs), which take the general linear dynamics of players into account. In the formulation, each player has local convex set constraints, and all players are restricted by coupling nonlinear inequality constraints. Notably, the majority of existing results for NGs with physical systems do not involve local constraints, let alone general convex sets. Besides, nearly all of related results cannot guarantee local constraints to be satisfied all the time, because physical players cannot control their decisions directly due to system dynamics. Here we develop a distributed adaptive strategy on the basis of gradient descent, projection operators, primal–dual methods and state feedback. The strategy is fully distributed. We analyze the strategy via variational analysis and Lyapunov theory. With our strategy, the players seek the exact variational generalized Nash equilibrium (v-GNE), and always satisfy local constraints, in contrast to existing results. Lastly, our method is applied to the electricity market games of doubly-fed induction generators.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112791"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145784447","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112782
Liwei An , Can Zhao , Guang-Hong Yang
This paper studies the problem of adaptive tracking control for nonlinear strict-feedback systems with parametric uncertainties and safety constraints. A co-design strategy of control barrier functions (CBFs) and barrier Lyapunov functions (BLFs) is proposed, which inherits the robustness and stability of traditional adaptive backstepping controllers. First, a safe virtual control signal is generated by the CBF-induced quadratic programming (QP), which is the suboptimal and smooth solution of the QP with a shifting function. Then, a BLF-based backstepping controller is designed by following the safe virtual control signal. It is shown that the co-design can minimize the damage to the original tracking performance on the premise of safety guarantees. The distinguishing point of the safety design over the existing results is to avoid constructing the high-order CBFs that lead to conservative feasible sets of inputs for ensuring high-relative-degree safety constraints. The simulation results show that the proposed scheme achieves better tracking performance compared with the existing high-order CBF-based method.
{"title":"CBF-based safety design for adaptive control of uncertain nonlinear strict-feedback systems","authors":"Liwei An , Can Zhao , Guang-Hong Yang","doi":"10.1016/j.automatica.2025.112782","DOIUrl":"10.1016/j.automatica.2025.112782","url":null,"abstract":"<div><div>This paper studies the problem of adaptive tracking control for nonlinear strict-feedback systems with parametric uncertainties and safety constraints. A co-design strategy of control barrier functions (CBFs) and barrier Lyapunov functions (BLFs) is proposed, which inherits the robustness and stability of traditional adaptive backstepping controllers. First, a safe virtual control signal is generated by the CBF-induced quadratic programming (QP), which is the suboptimal and smooth solution of the QP with a shifting function. Then, a BLF-based backstepping controller is designed by following the safe virtual control signal. It is shown that the co-design can minimize the damage to the original tracking performance on the premise of safety guarantees. The distinguishing point of the safety design over the existing results is to avoid constructing the high-order CBFs that lead to conservative feasible sets of inputs for ensuring high-relative-degree safety constraints. The simulation results show that the proposed scheme achieves better tracking performance compared with the existing high-order CBF-based method.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112782"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1016/j.automatica.2025.112758
Kaiyun Xie , Junlin Xiong
This paper investigates the existence and computability of the stationary Stackelberg equilibrium (SSE) in two-person zero-sum stochastic Stackelberg games (SSGs). First, an operator-based approach is developed to illustrate that such games admit a fixed-point equilibrium (FPE). It is further proven that the FPE strategy pair constitutes an SSE. Building on this foundation, a value iteration (VI) algorithm is proposed to compute the SSE strategies. However, due to the curse of dimensionality, the exact computation of SSE strategies involves high computational complexity. To address this issue, an -sacrifice strategy is introduced to approximate the leader’s SSE strategy by performing finite iterations, with the degree of approximation quantified by . The relationship between and the number of iterations is established, ensuring a trade-off between computational efficiency and strategic performance. An information flow control example demonstrates the efficiency of the designed strategies.
{"title":"Stationary Stackelberg equilibrium in two-person zero-sum stochastic Stackelberg games","authors":"Kaiyun Xie , Junlin Xiong","doi":"10.1016/j.automatica.2025.112758","DOIUrl":"10.1016/j.automatica.2025.112758","url":null,"abstract":"<div><div>This paper investigates the existence and computability of the stationary Stackelberg equilibrium (SSE) in two-person zero-sum stochastic Stackelberg games (SSGs). First, an operator-based approach is developed to illustrate that such games admit a fixed-point equilibrium (FPE). It is further proven that the FPE strategy pair constitutes an SSE. Building on this foundation, a value iteration (VI) algorithm is proposed to compute the SSE strategies. However, due to the curse of dimensionality, the exact computation of SSE strategies involves high computational complexity. To address this issue, an <span><math><mi>ϵ</mi></math></span>-sacrifice strategy is introduced to approximate the leader’s SSE strategy by performing finite iterations, with the degree of approximation quantified by <span><math><mi>ϵ</mi></math></span>. The relationship between <span><math><mi>ϵ</mi></math></span> and the number of iterations <span><math><mi>n</mi></math></span> is established, ensuring a trade-off between computational efficiency and strategic performance. An information flow control example demonstrates the efficiency of the designed strategies.</div></div>","PeriodicalId":55413,"journal":{"name":"Automatica","volume":"185 ","pages":"Article 112758"},"PeriodicalIF":5.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145799602","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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